Vacancies and precipitation

7.2.4 Vacancies and precipitation

It is clear that because precipitation is controlled by the rate of atomic migration in the alloy, tem- perature will have a pronounced effect on the process. Moreover, since precipitation is a thermally

400 Physical Metallurgy and Advanced Materials activated process, other variables such as time of annealing, composition, grain size and prior cold

work are also important. However, the basic treatment of age-hardening alloys is solution treatment followed by quenching, and the introduction of vacancies by the latter process must play an important role in the kinetic behavior.

It has been recognized that, near room temperature, zone formation in alloys such as aluminum– copper and aluminum–silver occurs at a rate many orders of magnitude greater than that calculated from the diffusion coefficient of the solute atoms. In aluminum–copper, for example, the formation of zones is already apparent after only a few minutes at room temperature, and is complete after an hour or two, so that the copper atoms must therefore have moved through several atomic spacings in that time. This corresponds to an apparent diffusion coefficient of copper in aluminum of about

10 −20 –10 −22 m 2 s −1 , which is many orders of magnitude faster than the value of 5 × 10 −29 m 2 s −1 obtained by extrapolation of high-temperature data. Many workers have attributed this enhanced diffusion to the excess vacancies retained during the quenching treatment. Thus, since the expression for the diffusion coefficient at a given temperature contains a factor proportional to the concentration of vacancies at that temperature, if the sample contains an abnormally large vacancy concentration

then the diffusion coefficient should be increased by the ratio c Q / c o , where c Q is the quenched-in vacancy concentration and c o is the equilibrium concentration. The observed clustering rate can be accounted for if the concentration of vacancies retained is about 10 −3 –10 −4 .

The observation of loops by transmission electron microscopy allows an estimate of the number of excess vacancies to be made, and in all cases of rapid quenching the vacancy concentration in these alloys is somewhat greater than 10 −4 , in agreement with the predictions outlined above. Clearly, as the excess vacancies are removed, the amount of enhanced diffusion diminishes, which agrees with the observations that the isothermal rate of clustering decreases continuously with increasing time. In fact, it is observed that D decreases rapidly at first and then remains at a value well above the equilibrium value for months at room temperature; the process is therefore separated into what is called the fast and slow reactions. A mechanism proposed to explain the slow reaction is that some of the vacancies quenched-in are trapped temporarily and then released slowly. Measurements show that the activation energy in the fast reaction ( ≈0.5 eV) is smaller than in the slow reaction (≈1 eV) by an amount which can be attributed to the binding energy between vacancies and trapping sites.

These traps are very likely small dislocation loops or voids formed by the clustering of vacancies. The equilibrium matrix vacancy concentration would then be greater than that for a well-annealed crystal by a factor exp[γ /rkT ], where γ is the surface energy, the atomic volume and r the radius of the defect (see Chapter 3). The experimental diffusion rate can be accounted for if r ≈ 2 nm, which is much smaller than the loops and voids usually seen, but they do exist. The activation energy for the

slow reaction would then be E D − (γ /r) or approximately 1 eV for r ≈ 2 nm. Other factors known to affect the kinetics of the early stages of ageing (e.g. altering the quenching rate, interrupted quenching and cold work) may also be rationalized on the basis that these processes lead to different concentrations of excess vacancies. In general, cold working the alloy prior to ageing causes a decrease in the rate of formation of zones, which must mean that the dislocations introduced by cold work are more effective as vacancy sinks than as vacancy sources. Cold working or rapid quenching therefore have opposing effects on the formation of zones. Vacancies are also important in other aspects of precipitation hardening. For example, the excess vacancies, by condensing to form

a high density of dislocation loops, can provide nucleation sites for intermediate precipitates. This leads to the interesting observation in aluminum–copper alloys that cold working or rapid quenching, by producing dislocations for nucleation sites, have the same effect on the formation of the θ ′ phase but, as we have seen above, the opposite effect on zone formation. It is also interesting to note that screw dislocations, which are not normally favorable sites for nucleation, can also become sites for preferential precipitation when they have climbed into helical dislocations by absorbing vacancies, and have thus become mainly of edge character. The long arrays of θ ′ phase observed in aluminum–copper alloys, shown in Figure 7.4c, have probably formed on helices in this way. In some

Mechanical properties II – Strengthening and toughening 401 of these alloys, defects containing stacking faults are observed, in addition to the dislocation loops

and helices, and examples have been found where such defects nucleate an intermediate precipitate having a hexagonal structure. In aluminum–silver alloys it is also found that the helical dislocations introduced by quenching absorb silver and degenerate into long narrow stacking faults on {1 1 1} planes; these stacking-fault defects then act as nuclei for the hexagonal γ ′ precipitate.

Many commercial alloys depend critically on the interrelation between vacancies, dislocations and solute atoms, and it is found that trace impurities significantly modify the precipitation process. Thus, trace elements which interact strongly with vacancies inhibit zone formation, e.g. Cd, In and Sn prevent zone formation in slowly quenched Al–Cu alloys for up to 200 days at 30 ◦

C. This delays the age-hardening process at room temperature, which gives more time for mechanically fabricating the quenched alloy before it gets too hard, thus avoiding the need for refrigeration. On the other hand, Cd increases the density of θ ′ precipitate by increasing the density of vacancy loops and helices which act as nuclei for precipitation and by segregating to the matrix/θ ′ interfaces, thereby reducing the interfacial energy.

Since grain boundaries absorb vacancies, in many alloys there is a grain boundary zone relatively free from precipitation. The Al–Zn–Mg alloy is one commercial alloy which suffers grain boundary weakness, but it is found that trace additions of Ag have a beneficial effect in refining the precipitate structure and removing the precipitate free grain boundary zone. Here it appears that Ag atoms stabi- lize vacancy clusters near the grain boundary and also increase the stability of the GP zone, thereby raising the GP zone solvus temperature. Similarly, in the ‘Concorde’ alloy, RR58 (basically Al– 2.5Cu–1.2Mg with additions), Si addition (0.25Si) modifies the as-quenched dislocation distribution, inhibiting the nucleation and growth of dislocation loops and reducing the diameter of helices. The

S-precipitate (Al 2 CuMg) is homogeneously nucleated in the presence of Si rather than heteroge- neously nucleated at dislocations, and the precipitate grows directly from zones, giving rise to improved and more uniform properties.

Apart from speeding up the kinetics of ageing, and providing dislocations nucleation sites, vacan- cies may play a structural role when they precipitate cooperatively with solute atoms to facilitate the basic atomic arrangements required for transforming the parent crystal structure to that of the product phase. In essence, the process involves the systematic incorporation of excess vacancies, produced by the initial quench or during subsequent dislocation loop annealing, in a precipitate zone or plate to change the atomic stacking. A simple example of θ ′ formation in Al–Cu is shown schematically in Figure 7.12. Ideally, the structure of the θ ′′ phase in Al–Cu consists of layers of copper on {1 0 0} separated by three layers of aluminum atoms. If a next-nearest neighbor layer of aluminum atoms from the copper layer is removed by condensing a vacancy loop, an embryonic θ ′ unit cell with Al in the

correct AAA … stacking sequence is formed (Figure 7.12b). Formation of the final CuAl 2 θ ′ fluorite structure requires shuffling only half of the copper atoms into the newly created next-nearest neighbor space and concurrent relaxation of the Al atoms to the correct θ ′ interplanar distances (Figure 7.12c).

The structural incorporation of vacancies in a precipitate is a non-conservative process, since atomic sites are eliminated. There exist equivalent conservative processes in which the new precipitate structure is created from the old by the nucleation and expansion of partial dislocation loops with predominantly shear character. Thus, for example, the BABAB {1 0 0} plane stacking sequence of the fcc structure can be changed to BAABA by the propagation of an a/2 {1 0 0} plane, or to BAAAB by the propagation of a pair of a/2 adjacent planes. Again, the AAA stacking resulting from the double shear is precisely that required for the embryonic formation of the fluorite structure from the fcc lattice.

In visualizing the role of lattice defects in the nucleation and growth of plate-shaped precipitates, a simple analogy with Frank and Shockley partial dislocation loops is useful. In the formation of a Frank loop, a layer of hcp material is created from the fcc lattice by the (non-conservative) condensation of

a layer of vacancies in {1 1 1}. Exactly the same structure is formed by the (conservative) expansion of a Shockley partial loop on a {1 1 1} plane. In the former case a semi-coherent ‘precipitate’

402 Physical Metallurgy and Advanced Materials u⬙⫺ CuAI 3 u⬘⫺ CuAI 2

a ⫽ 4.04 Å, c ⫽ 7.68 Å

a ⫽ 4.04 Å, c ⫽ 5.80 Å

c 2.90 2.02 2.02 c

1.82 a a a a a a

(c) Figure 7.12 Schematic diagram showing the transition of θ ′′ to θ ′ in Al–Cu by the vacancy

(a)

(b)

mechanism. Vacancies from annealing loops are condensed on a next-nearest Al plane from the copper layer in θ ′′ to form the required AAA Al stacking. Formation of the θ ′ fluorite structure then requires only slight redistribution of the copper atom layer and relaxation of the Al layer spacings (courtesy of K. H. Westmacott).

0.5 ␮m

Figure 7.13 The formation of semi-coherent Cu needles in Fe–1% Cu (courtesy of K. H. Westmacott).

is produced bounded by an a/3 an a/6 of processes. Of course, formation of the final precipitate structure requires, in addition to these structural rearrangements, the long-range diffusion of the correct solute atom concentration to the growing interface.

The growth of a second-phase particle with a disparate size or crystal structure relative to the matrix is controlled by two overriding principles – the accommodation of the volume and shape change, and the optimized use of the available deformation mechanisms. In general, volumetric transformation strains are accommodated by vacancy or interstitial condensation, or prismatic dislo- cation loop punching, while deviatoric strains are relieved by shear loop propagation. An example is shown in Figure 7.13. The formation of semi-coherent Cu needles in Fe–1% Cu is accomplished by the generation of shear loops in the precipitate/matrix interface. Expansion of the loops into the matrix and incorporation into nearby precipitate interfaces leads to a complete network of dislocations interconnecting the precipitates.

Mechanical properties II – Strengthening and toughening 403